Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
528 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #31771080 | C2 | semidirect |
| 2. #31770717 | C2 | semidirect |
| 3. D8×Dic269 | C2 | semidirect |
| 4. #31770643 | C2 | semidirect |
| 5. #31770610 | C2 | semidirect |
| 6. #31770560 | C2 | semidirect |
| 10. D4×Dic269 | C22 | semidirect |
| 14. #22575387 | C22 | semidirect |
| 15. #22575385 | C22 | semidirect |
| 16. #22575374 | C22 | semidirect |
| 17. #22575363 | C22 | semidirect |
| 18. C8×Dic269 | C22 | semidirect |
| 20. C2×D8×C269 | C4 | semidirect |
| 37. C2×D4×C269 | C2×C4 | semidirect |
| 40. D8×C269 | C2×C4 | semidirect |
| 41. D8×C269 | C2×C4 | semidirect |
| 42. C2×C8×C269 | C2×C4 | semidirect |
| 77. C269 | #2948 | semidirect |
| 87. C2×D8 | Dic269 | semidirect |
| 105. C2×D4 | C2×Dic269 | semidirect |
| 109. D8 | C2×Dic269 | semidirect |
| 110. D8 | C2×Dic269 | semidirect |
| 113. C2×C8 | C2×Dic269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771080 | 2 |
| #31770717 | 2 |
| D8×Dic269 | 2 |
| #31770643 | 2 |
| #31770610 | 2 |
| #31770560 | 2 |
| C22×D8×C269 | 2 |
| #2948 | 269 |